A new approach to the covering radius of codes
β Scribed by N.J.A Sloane
- Book ID
- 107885028
- Publisher
- Elsevier Science
- Year
- 1986
- Tongue
- English
- Weight
- 987 KB
- Volume
- 42
- Category
- Article
- ISSN
- 0097-3165
No coin nor oath required. For personal study only.
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A new quaternary linear code of length 19, codimension 5, and covering radius 2 is found in a computer search using tabu search, a local search heuristic. Starting from this code, which has some useful partitioning properties, di!erent lengthening constructions are applied to get an in"nite family o
We present lower and upper bounds on the covering radius of Reed-Muller codes, yielding asymptotical improvements on known results. The lower bound is simply the sphere covering one (not very new). The upper bound is derived from a thorough use of a lemma, the 'essence of Reed-Mullerity'. The idea